An electrostatically actuated oscillator of micro- or nano-electromechanical system type, respectively MEMS or NEMS, is a device including a moveable element that can be set to oscillate.
Such oscillators consume little energy and have a reduced size. They thus find particularly advantageous application in nomadic objects such as smartphones or tablet computers. These oscillators are in particular used to manufacture inertial sensors, such as accelerometers or gyroscopes, intended to equip such objects.
A nomadic objet may moreover be equipped with a global positioning system (GPS) which consumes a lot of energy. Inertial sensors make it possible to calculate in real time the movements of the object and thus to reduce resorting to the global positioning system. The latter remains however useful for determining a reference position of the object, for example at regular time intervals.
The electrostatically actuated oscillator comprises actuating means which transform an excitation signal applied at the input of the oscillator into an electrostatic actuating force, also called “excitation force”, acting on the moveable element. The movements of the moveable element are measured by detection means which generate a response signal at the output of the oscillator. The excitation signal and the response signal are for example in the form of voltages.
The oscillator is notably characterised by a quality factor which is a parameter that has an influence on the precision of the inertial sensor. An oscillator with a high quality factor makes it possible to obtain a more precise inertial sensor, which makes it possible to resort less frequently to the global positioning system and thus to reduce electrical energy consumption.
It is thus important to measure the quality factor of the oscillator, notably to validate the development and the manufacture of the inertial sensor.
A first method for measuring the quality factor consists in exciting the oscillator by means of a sinusoidal excitation voltage of frequency F0 and in measuring the amplitude of the oscillations at the frequency 2F0. The amplitude of the oscillations is measured at the frequency 2F0 because the actuating force is proportional to the square of the excitation voltage. By sweeping a frequency range, an amplitude spectral density of the oscillations is obtained which includes a resonance peak having an amplitude maximum reached at the resonance frequency of the oscillator. The quality factor may then be determined from the width of the resonance peak considered at half of its height.
A drawback of this measurement method by frequency sweeping is that in order to measure the amplitude of the oscillations correctly, the oscillator has to recover an idle position between two successive measurements. The time necessary for the oscillator to recover its idle position after excitation is approximately equal to three times a damping constant which is proportional to the quality factor. Considering for example a quality factor of the order of 106, the damping constant is of the order of 10 seconds. In this case, for example more than 2 hours are needed to acquire 250 measurement points.
Furthermore, the precision with which the resonance peak is defined depends on the number of measurement points. If the number of points is not sufficient, the resonance peak may be widened artificially and its amplitude maximum may be frequency shifted, which distorts the measurement of the quality factor.
The time necessary to implement this measurement method is thus a factor limiting productivity, all the more since the current trend is to increase the quality factor of oscillators. This measurement time does not make it reasonably possible, in particular from an industrial viewpoint, to characterise all of the oscillators of a silicon wafer, which generally comprises more than one hundred thereof. Only several oscillators are then characterised, which makes it difficult to estimate a manufacturing efficiency of the oscillators.
The quality factor may also be determined by measuring the logarithmic decrement of the amplitude of the oscillations of the oscillator. This measurement method consists in applying an excitation signal at the input of the oscillator then in acquiring the response signal present at the output of the oscillator after having stopped the excitation of the oscillator.
The measurement of the logarithmic decrement may be carried out using as excitation signal a sinusoidal voltage at the resonance frequency. In this case, a drawback is that it is necessary to parameterise the frequency of the sinusoidal voltage with precision. Indeed, if the frequency of the sinusoidal voltage deviates too far from the resonance frequency, the amplitude of the oscillations risks being too low to enable a correct measurement.
FIG. 1 illustrates the relationship that exists between the quality factor and the precision required to adjust the frequency of the excitation signal. FIG. 1 represents the amplitude spectral density (ASD) of the response voltage of three oscillators of which the resonance frequency is equal to 85 kHz and of which the quality factor Q is respectively equal to 104, 105 and 106. The spectral width ΔF of the resonance peak when the amplitude is divided by a factor 10 with respect to the amplitude maximum is considered. This spectral width ΔF, which represents the tolerance on the value that the frequency of the excitation signal can take, is equal to around 400, respectively 40 and 4, parts per million of the resonance frequency when the quality factor is equal to 104, respectively 105 and 106.
Another drawback is that the resonance frequency of the oscillator varies as a function of the experimental conditions, notably as a function of the temperature and the mounting for the measurement. The variation in the resonance frequency can reach 5000 parts per million. Consequently, it is necessary to search for the resonance frequency before each measurement of the quality factor, which wastes a lot of time. In addition, when the resonance frequency of the oscillator varies rapidly, it may be difficult to string together sufficiently rapidly the localisation of the resonance frequency and the measurement of the logarithmic decrement.
The measurement of the logarithmic decrement may also be carried out using as excitation signal a voltage pulse. Indeed, a pulse in the time domain corresponds to a constant amplitude in the frequency domain. In practice, the pulse rather has a wide spectral band width. By ensuring that the resonance frequency of the oscillator is included in the spectral width of the pulse, it is possible to excite the oscillator without it being necessary to know precisely the resonance frequency.
However, a drawback of this method is that the higher the resonance frequency of the oscillator, the lower the amplitude spectral density of the excitation signal because the spectral width of the excitation signal must be greater than the resonance frequency. This phenomenon is highlighted in FIGS. 2A and 2B.
FIG. 2A shows an example of a voltage pulse in the form of a cardinal sine function, the voltage pulse u(t) being defined by the following equation:u(t)=A·sin c(ΔF·t)  (1)where A and ΔF are respectively the amplitude and the spectral band width of the excitation signal. FIG. 2 represents a first signal having a first spectral width ΔF1 of 100 Hz and a second signal having a second spectral width ΔF2 of 10 Hz.
FIG. 2B shows the amplitude spectral density of the signals of FIG. 2A. When the spectral width is multiplied by a factor 10, the amplitude spectral density is divided by a factor 10. Consequently, if the resonance frequency of the oscillator is high, for example of the order of several tens of kilohertz, the electrostatic force generated by the voltage pulse is too weak to excite the oscillator so as to enable a measurement of the amplitude of the oscillations.